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The IEEE 802.11e standard revises the Medium Access Control (MAC) layer of the former IEEE 802.11 standard for Quality-of-Service (QoS) provision in the Wireless Local Area Networks (WLANs). The Enhanced Distributed Channel Access (EDCA) function of 802.11e defines multiple Access Categories (AC) with AC-specific Contention Window (CW) sizes, Arbitration Interframe Space (AIFS) values, and Transmit Opportunity (TXOP) limits to support MAC-level QoS and prioritization. We propose an analytical model for the EDCA function which incorporates an accurate CW, AIFS, and TXOP differentiation at any traffic load. The proposed model is also shown to capture the effect of MAC layer buffer size on the performance. Analytical and simulation results are compared to demonstrate the accuracy of the proposed approach for varying traffic loads, EDCA parameters, and MAC layer buffer space.